Question

An input voltage represented by waveform as shown below is applied to a moving iron instrument. The reading of the instrument will be _______ V.

• A. 1.0
• B. 0.132
• C. 1.32
• D. 0.32

Answer 1

The correct option is C 1.32


Input waveform shown in the question is periodic waveform with time period of 2 $\Omega$.
Moving iron instrument reads rms value

$V_{rms\left(meter\right)}=\sqrt{\frac{1}{T_0}{\int }_0^{T_0}{V}^2\left(t\right)dt}$

$=\sqrt{\frac{1}{2\pi }{\int }_0^{\pi /2}{\left(2\right)}^2+{\int }_{\pi /2}^{2\pi }{(-1)}^{2}dt}$

$=\sqrt{\frac{1}{2\pi }[4(\frac{\pi }{2}-0)+1(2\pi -\frac{\pi }{2})]}$

$=\sqrt{\frac{1}{2\pi }[2\pi +\frac{3\pi }{2}]}=\sqrt{\frac{1}{2\pi }\times \frac{7\pi }{2}}$

$=\frac{\sqrt{7}}{2}=1.32$